中文摘要：

在两轮自平衡车平面轨迹的鲁棒最优跟踪问题的研究中，由于在存在外界干扰等不确定性时，为保证平衡车保持车体平衡的同时最优跟踪参考轨迹，引人滑模控制对最优跟踪控制器进行鲁棒化设计。将平衡车不确定系统的最优跟踪问题转化为一类增广系统的最优调节问题，采用一种带有状态变量积分项的新型切换函数对增广系统设计最优滑模输出跟踪控制器，证明系统的理想滑动模态与标称系统的最优动态方程相一致。仿真结果表明，所设计的控制器对于由外系统给出的参考信号能够实现精确跟踪，对于外界干扰等不确定性具有完全鲁棒性，动态性能优于传统的最优跟踪控制。

英文摘要：

The robust optimal tracking problem of plane trajectory for two-wheeled self-balancing car is studied. The sliding mode control is introduced into the robust design for the optimal tracking controller to guarantee the car body to keep balance and track the reference trajectory optimally in the case of uncertainties such as external interference. The optimal tracking problem of self-balancing car＇s uncertain system is transformed into an optimal adjusting problem of a class of augmented systems. The optimal sliding mode tracking controller is designed for the augmented system by using a kind of new switch function with the intergral term of state variables. It is proposed that the ideal sliding-mode of the system is consistent with the optimal dynamical equation of the nominal system. Simulation resuits show that the controller can track the reference signal given by exosystems accurately and is completely robust for the uncertainties such as external interference. The systems dynamic performance is better than the traditional optimal tracking controller.